Question

Simplify and write the answer in the exponential form.
${\left(4\right)}^{-3}\times {\left(5\right)}^{-3}\times {(-5)}^{-3}$
[2 marks]

Answer 1

${(-4)}^{-3}\times {\left(5\right)}^{-3}\times {(-5)}^{-3}\mathrm{Since},\mathrm{the}\mathrm{power}\mathrm{is}\mathrm{same}\mathrm{for}\mathrm{whole}\mathrm{expression}\mathrm{so}\mathrm{with}\mathrm{the}\mathrm{help}\mathrm{of}\mathrm{laws}\mathrm{of}\mathrm{exponent}{a}^m\times b^m={\left(\mathrm{ab}\right)}^m\Rightarrow {(-4)}^{-3}\times {\left(5\right)}^{-3}\times {(-5)}^{-3}={(-4\times 5\times -5)}^{-3}\left[1\mathrm{mark}\right]\Rightarrow (100{)}^{-3}=\frac{1}{{100}^3}\{a^{-m}=\frac{1}{a^m}\left\}\right[1\mathrm{mark}]$